Question

A photographer uses his camera, whose lens has a 50 mm focal length, to focus on an object 1.5 m away. He then wants to take a picture of an object that is 30 cm away.

How far must the lens move to focus on this second object?

Answer 1

The distance is
`z = 0.008 \ m`

Step-by-step explanation:

From the question we are told that

The focal length is
`f = 50 \ mm = 50*10^(-3) \ m`

Generally the lens equation is mathematically represented as

`(1)/(u) + (1)/(v) = (1)/(f)`

At image distance u = 1.5 m

`(1)/(1.5) + (1)/(v) = (1)/(50 *10^(-3))`

=>
`(1)/(50 *10^(-3)) - (1)/(1.5) = (1)/(v)`

=>
`v = 0.052 \ m`

At image distance
`u = 30\ cm = 0.30 \ m`

`(1)/(0.3) + (1)/(v_1) = (1)/(50 *10^(-3))`

=>
`(1)/(50 *10^(-3)) - (1)/(0.30 ) = (1)/(v_1)`

=>
`v_1 = 0.06 \ m`

The distance the lens need to move is evaluate as

`z = |v - v_1|`

`z = |0.052 - 0.06|`

`z = 0.009 \ m`